An approximate nerve theorem
Event details
| Date | 23.02.2016 |
| Hour | 10:15 › 11:30 |
| Speaker |
Primoz Skraba (Artificial Intelligence Laboratory, Jozej Stefan Institute, Ljubljana) |
| Location |
CM113
|
| Category | Conferences - Seminars |
The nerve theorem [Borsuk 48] states that the homotopy type of a sufficiently nice topological space is captured by the nerve of a good cover of that space. In the case of persistence, we rarely compute the persistence diagram of a filtration exactly, but rather an approximation of it. In this talk we introduce the notion of an epsilon-good cover and its application to computing persistence. Rather than require a good cover, one where all the elements of the cover and their finite intersections are contractible, we define the notion of an epsilon good cover - one where its all elements and finite intersections are homologically trivial modulo epsilon-persistent classes (i.e. each element can have a small amount of topological noise). We show an approximation result for the persistence diagram of a filtration of the nerve and the underlying space which depends on epsilon and the maximal dimension of the nerve and show that this bound is tight.
Links
Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek